Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D4×#64423 |
| Fitting | C72×D4 ⋊ C2×C3 |
| Hall | C7×D4×D7 ⋊ C3 |
| Hall | #3861 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#64423 |
| commutator, socle, cosocle | C2×C72 | C23×C3 |
| Fitting | C72×D4 | C2×C3 |
| hypercenter | D4 | #64423 |
| hypocenter | C72 | C2×C3×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2 ◁ D4 | |
264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
85 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#64423⋊C2, #72214216, #72214244, … |
| maximal normal subgroup of | D4×#64423⋊C2, #72214216, #72214244, … |
| maximal quotient of | #72214858, C2×D4×#64423 |
Past the SmallGroups library coverage — no SmallGroups id.